// Magma code for the lmfdb family of higher genus curves 15.93-1.0.3-3-31.1
// The results are stored in a list of records called 'data'

RecFormat:=recformat<group,gp_id, signature,gen_vectors,conj_classes,genus,dimension,r,g0, passport_label,gen_vect_label, is_hyperelliptic, hyp_involution, is_cyclic_trigonal,cyc_auto,full_auto, full_sign,topological_class,braid_class>;

data:=[];

// Create group as a permutation group, and generate data which is the same for all entries.
gp_id:=[93,1];
H:=SmallGroup(gp_id[1],gp_id[2]); n:=#H; LP:=[]; LG:=[g : g in H]; for i in [1..n] do x:=LG[i]; Tx:=[LG[j]*x : j in [1..n]]; permL:=[]; for j in [1..n] do for k in [1..n] do if Tx[j] eq LG[k] then permL[j]:=k;  break; end if; end for; end for; Append(~LP,permL); end for; G:=PermutationGroup<n|LP>; 
signature:=[0,3,3,31];
genus:=15;
r:=#signature-1;
g0:=signature[1];
dim:=3*g0-3+r;
S:=Sym(gp_id[1]);

// Here we add an action to data.
gen_vectors:=[[32, 57, 51, 45, 39, 33, 58, 52, 46, 40, 34, 59, 53, 47, 41, 35, 60, 54, 48, 42, 36, 61, 55, 49, 43, 37, 62, 56, 50, 44, 38, 63, 88, 82, 76, 70, 64, 89, 83, 77, 71, 65, 90, 84, 78, 72, 66, 91, 85, 79, 73, 67, 92, 86, 80, 74, 68, 93, 87, 81, 75, 69, 1, 26, 20, 14, 8, 2, 27, 21, 15, 9, 3, 28, 22, 16, 10, 4, 29, 23, 17, 11, 5, 30, 24, 18, 12, 6, 31, 25, 19, 13, 7], [93, 67, 72, 77, 82, 87, 92, 66, 71, 76, 81, 86, 91, 65, 70, 75, 80, 85, 90, 64, 69, 74, 79, 84, 89, 63, 68, 73, 78, 83, 88, 31, 5, 10, 15, 20, 25, 30, 4, 9, 14, 19, 24, 29, 3, 8, 13, 18, 23, 28, 2, 7, 12, 17, 22, 27, 1, 6, 11, 16, 21, 26, 62, 36, 41, 46, 51, 56, 61, 35, 40, 45, 50, 55, 60, 34, 39, 44, 49, 54, 59, 33, 38, 43, 48, 53, 58, 32, 37, 42, 47, 52, 57], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 1, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 32, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 63]];
cc:=[2,3,4];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);
